Statistics and Probability Commons^™

Sparse Domination Of The Martingale Transform, Michael Scott Kutzler

Mathematics & Statistics ETDs

Linear operators are of huge importance in modern harmonic analysis. Many operators can be dominated by finitely many sparse operators. The main result in this thesis is showing a toy operator, namely the Martingale Transform is dominated by a single sparse operator. Sparse operators are based on a sparse family which is simply a subset of a dyadic grid. We also show the A2 conjecture for the Martingale Transform which follows from the sparse domination of the Martingale Transform and the A2 conjecture for sparse operators.

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An Introduction To Calling Bullshit: Learning To Think Outside The Black Box, Jevin D. West, Carl T. Bergstrom

Numeracy

Bergstrom, Carl T. and Jevin D. West. 2020. Calling Bullshit: The Art of Skepticism in a Data-Driven World. (New York: Random House) 336 pp. ISBN 978-0525509202.

While statistical methods receive greater attention, the art of critically evaluating information in everyday life more commonly depends on thinking outside the black box of the algorithm. In this piece we introduce readers to our book and associated online teaching materials—for readers who want to more capably call “bullshit” or to teach their students to do the same.

Decision Based Learning Course Design & Implementation For Introductory Statistics, Austin Heath

Undergraduate Honors Theses

Researchers in multiple industries (biomedicine, engineering, etc.) cite the selection of an appropriate statistical test as a common problem. Experts draw on a framework of conceptual and procedural knowledge to navigate when to use statistical methods. Students also struggle determining the correct statistical method to use for a given research question. This is because they lack the opportunity to practice recognizing a host of features in each research question that provide clues for experts as to which method is most appropriate. “Decision Based Learning” (DBL) is a teaching method designed to help teachers and students address this struggle. In this …

Lapatinib And Poziotinib Overcome Abcb1-Mediated Paclitaxel Resistance In Ovarian Cancer, J. Robert Mccorkle, Justin W. Gorski, Jinpeng Liu, Mckayla J. Riggs, Anthony B. Mcdowell Jr., Nan Lin, Chi Wang, Frederick R. Ueland, Jill M. Kolesar

Markey Cancer Center Faculty Publications

Conventional frontline treatment for ovarian cancer consists of successive chemotherapy cycles of paclitaxel and platinum. Despite the initial favorable responses for most patients, chemotherapy resistance frequently leads to recurrent or refractory disease. New treatment strategies that circumvent or prevent mechanisms of resistance are needed to improve ovarian cancer therapy. We established in vitro paclitaxel-resistant ovarian cancer cell line and organoid models. Gene expression differences in resistant and sensitive lines were analyzed by RNA sequencing. We manipulated candidate genes associated with paclitaxel resistance using siRNA or small molecule inhibitors, and then screened the cells for paclitaxel sensitivity using cell viability assays. …

Associations Between Fasting Duration, Timing Of First And Last Meal, And Cardiometabolic Endpoints In The National Health And Nutrition Examination Survey, Michael David Wirth, Longgang Zhao, Gabrielle Turner-Mcgrievy, Andrew Ortaglia

Faculty Publications

Background: Research indicates potential cardiometabolic benefits of energy consumption earlier in the day. This study examined the association between fasting duration, timing of first and last meals, and cardiometabolic endpoints using data from the National Health and Nutrition Examination Survey (NHANES). Methods: Cross-sectional data from NHANES (2005–2016) were utilized. Diet was obtained from one to two 24-h dietary recalls to characterize nighttime fasting duration and timing of first and last meal. Blood samples were obtained for characterization of C-reactive protein (CRP); glycosylated hemoglobin (HbA1c %); insulin; glucose; and high-density lipoprotein (HDL), low-density lipoprotein (LDL), and total cholesterol. Survey design procedures …

Dynamics Of Plane Waves In The Fractional Nonlinear Schrödinger Equation With Long-Range Dispersion, Siwei Duo, Taras I. Lakoba, Yanzhi Zhang

Mathematics and Statistics Faculty Research & Creative Works

We analytically and numerically investigate the stability and dynamics of the plane wave solutions of the fractional nonlinear Schrödinger (NLS) equation, where the long-range dispersion is described by the fractional Laplacian (−∆)α/2 . The linear stability analysis shows that plane wave solutions in the defocusing NLS are always stable if the power α ∈ [1, 2] but unstable for α ∈ (0, 1). In the focusing case, they can be linearly unstable for any α ∈ (0, 2]. We then apply the split-step Fourier spectral (SSFS) method to simulate the nonlinear stage of the plane waves dynamics. In agreement with …

Ensemble Data Fitting For Bathymetric Models Informed By Nominal Data, Samantha Zambo

Dissertations

Due to the difficulty and expense of collecting bathymetric data, modeling is the primary tool to produce detailed maps of the ocean floor. Current modeling practices typically utilize only one interpolator; the industry standard is splines-in-tension.

In this dissertation we introduce a new nominal-informed ensemble interpolator designed to improve modeling accuracy in regions of sparse data. The method is guided by a priori domain knowledge provided by artificially intelligent classifiers. We recast such geomorphological classifications, such as ‘seamount’ or ‘ridge’, as nominal data which we utilize as foundational shapes in an expanded ordinary least squares regression-based algorithm. To our knowledge …

Confluent Projections And Connectedness Of Inverse Limits, Włodzimierz J. Charatonik, Daria Michalik

Mathematics and Statistics Faculty Research & Creative Works

V. Nall proved that connectedness is preserved under inverse limits if the bounding functions are unions of functions with connected images. We show that for such functions the projections from the graph onto domain are confluent and we investigate relationships between functions satisfying this or similar conditions with confluence or openness of projections.

Conditional And Marginal Imputation Models For Multilevel Data, Gang Liu

Legacy Theses & Dissertations (2009 - 2024)

This dissertation study extends sequential hierarchical regression imputation (SHRIMP) methods to multilevel datasets with three levels of nesting and proposes a marginal method based on marginalized multilevel model (MMM) framework. Specifically, the proposed model consists of two levels such that the first level relates the marginal mean of responses with covariates through a generalized regression model and the second level includes subject specific random effects within the same generalized regression model. To draw the inference on the population-averaged or subject-specified coefficients, the hierarchical regression and/or MMM is applied as the imputation and estimation models. We employ Markov Chain Monte Carlo …

Impact Of Inconsistent Imputation Models In Mediation Analysis, Bo Ye

Legacy Theses & Dissertations (2009 - 2024)

In this dissertation, we study the impact of inconsistent imputation methods in mediation analysis and its application. We present the study in three papers.

Performance Comparison Of Imputation Methods For Mixed Data Missing At Random With Small And Large Sample Data Set With Different Variability, Kyei Afari

Electronic Theses and Dissertations

One of the concerns in the field of statistics is the presence of missing data, which leads to bias in parameter estimation and inaccurate results. However, the multiple imputation procedure is a remedy for handling missing data. This study looked at the best multiple imputation methods used to handle mixed variable datasets with different sample sizes and variability along with different levels of missingness. The study employed the predictive mean matching, classification and regression trees, and the random forest imputation methods. For each dataset, the multiple regression parameter estimates for the complete datasets were compared to the multiple regression parameter …

Applying Deep Learning To The Ice Cream Vendor Problem: An Extension Of The Newsvendor Problem, Gaffar Solihu

Electronic Theses and Dissertations

The Newsvendor problem is a classical supply chain problem used to develop strategies for inventory optimization. The goal of the newsvendor problem is to predict the optimal order quantity of a product to meet an uncertain demand in the future, given that the demand distribution itself is known. The Ice Cream Vendor Problem extends the classical newsvendor problem to an uncertain demand with unknown distribution, albeit a distribution that is known to depend on exogenous features. The goal is thus to estimate the order quantity that minimizes the total cost when demand does not follow any known statistical distribution. The …

Factors Influencing Student Outcomes In A Large, Online Simulation-Based Introductory Statistics Course, Ella M. Burnham

Department of Statistics: Dissertations, Theses, and Student Research

The demand for statistical knowledge and skills is growing in many disciplines, so more students are enrolling in introductory statistics courses (Blair, Kirkman, & Maxwell, 2018). At the same time, institutions are seeking course delivery methods that allow for greater flexibility for students, especially following the onset of the COVID-19 pandemic; therefore, there is more interest in the development and delivery of online introductory statistics courses.

To address this, I collaboratively designed an online introductory statistics course which focuses on simulation-based inference for the University of Nebraska-Lincoln. The course design was informed by the Community of Inquiry framework (Garrison, Anderson, …

Housing Variables And Immigration: An Exploratory And Predictive Data Analysis In New York City, Jhonatan Medri Cobos

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The relationship between housing and immigration has become relevant in the U.S., especially in a highly populated metropolis such as New York City (NYC). Determining whether immigration status affects home ownership percentage, household rent, or housing cost percentage could help understand the quality of life of NYC residents. Graphical exploration, spatial dependence tests, and spatial autoregressive models of housing and immigration variables provide some insights about their relationships. Our exploration takes place at some geographic subareas of NYC.

Our results first indicate that the housing and immigration data reports spatial dependence; values of a geographic subarea are related to values …

Significant Gene Array Analysis And Cluster-Based Machine Learning For Disease Class Prediction, Myrine A. Barreiro-Arevalo

Theses and Dissertations

Gene expression analysis has been of major interest to biostatisticians for many decades. Such studies are necessary for the understanding of disease risk assessment and prediction, so that medical professionals and scientists alike may learn how to better create treatment plans to lessen symptoms and perhaps even find cures. In this study, we will investigate various gene expression analyses and machine learning techniques for disease class prediction, as well as assess predictive validity of these models and uncover differentially expressed (DE) genes for their relevant pathology datasets. Multiple gene expression datasets will be used to test model accuracies and will …

Predictive Modeling Of Clinical Outcomes For Hospitalized Covid-19 Patients Utilizing Cytof And Clinical Data., Onajia Stubblefield

Electronic Theses and Dissertations

In December 2019, an outbreak of a novel coronavirus initiated a global pandemic. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a virus that causes the disease coronavirus disease 2019 (COVID-19). Symptoms of infection with COVID-19 vary widely between individuals. While some infected individuals are asymptomatic, others need more extensive care and require hospitalization. Indeed, the COVID-19 pandemic was characterized by a shortage of hospital beds which presented additional complications in providing adequate care for patients. In this study, we used a combination of T cell population data collected from mass cytometry analysis and clinical markers to form a predictive …

Identification And Characterization Of De Novo Germline Tp53 Mutation Carriers In Families With Li-Fraumeni Syndrome, Carlos C. Vera Recio

Dissertations and Theses (Open Access)

Li-Fraumeni syndrome (LFS) is an inherited cancer syndrome caused by a deleterious mutation in TP53. An estimated 48% of LFS patients present due to a de novo mutation (DNM) in TP53. The knowledge of DNM status, DNM or familial mutation (FM), of an LFS patient requires genetic testing of both parents which is often inaccessible, making de novo LFS patients difficult to study. Famdenovo.TP53 is a Mendelian Risk prediction model used to predict DNM status of TP53 mutation carriers based on the cancer-family history and several input genetic parameters, including disease-gene penetrance. The good predictive performance of Famdenovo.TP53 was demonstrated …

Predicting Severity Of Traumatic Brain Injury: A Residual Learning Model From Magnetic Resonance Images, Dacosta Yeboah

Graduate Theses/Dissertations

One of the most significant frontiers for computational scientists is the engineering of human healthcare delivery based on intelligent analysis of health data. In a variety of neurological disorders such as Traumatic Brain Injury (TBI), neuro-imaging information plays a crucial role in the decision-making regarding patient care and as a potential prognostic marker for outcome. TBI is a heterogeneous neurological disorder. Due to the economic burdens of the disorder, sorting out this heterogeneity could provide more insights and better understanding of TBI recovery trajectories, thus improving overall diagnosis and treatment options. Magnetic Resonance Imaging (MRI) is a non-invasive technique that …

Prediction Intervals: The Effects And Identification Of Sparse Regions For Nonparametric Regression Methods, Jackson Faires

Electronic Theses and Dissertations

In this work, we provide an overview of different nonparametric methods for prediction interval estimation and investigate how well they perform when making predictions in sparse regions of the predictor space. This sparsity is an extension to the more common concept of extrapolation in linear regression settings. Using simulation studies, we show that coverage probabilities using prediction intervals from quantile k-nearest neighbors and quantile random forest can be biased to low or too high from the nominal level under various situations of sparsity. We also introduce a test that can be used to see if a new data point lies …

Glivenko-Cantelli Theorems For Integrated Functionals Of Stochastic Processes, Jia Li, Congshan Zhang, Yunxiao Liu

Research Collection School Of Economics

We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Hölder classes as special cases. The general Glivenko-Cantelli theorem is then applied in more concrete high-frequency statistical settings to establish uniform convergence results for general integrated functionals of the volatility of efficient price and local moments of microstructure noise.